A point \( s \) of a closed con­vex sub­set \( S \) of \( k \)-space is ad­miss­ible if there is no \( t\in S \) with \( t_i\leq s_i \) for all \( i=1,\dots \), \( k \), \( t\neq s \). An ex­ample is giv­en in which the set \( A \) of ad­miss­ible points is not closed.

Let \( P \) be the set of vec­tors \( p=(p_1,\dots \), \( p_k) \) with \( p_i > 0 \) and \( \sum_1^k p_i=1 \), let \( B(p) \) be the set of \( s\in S \) with
\[ (p,s)=\min_{t\in S}(p,t) ,\]
and let \( B=\sum B(p) \), so that \( B \) con­sists of ex­actly those points of \( S \) at which there is a sup­port­ing hy­per­plane whose nor­mal has pos­it­ive com­pon­ents.

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